Calculating steady-state probabilities of single-channel closed queueing systems using hyperexponential approximation

An algorithm for calculating steady state probabilities of $M|E_r|c|K$ queueing systems

This paper presents a method for calculating steady state probabilities of M |Er|c|K queueing systems. The infinitesimal generator matrix is used to define all possible states in the system and their transition probabilities. While this matrix can be written down immediately for many other M |PH |c|K queueing systems with phase-type service times (e.g. Coxian, Hypoexponential, . . . ), it requi...

Steady State Probabilities of a Three Preemptive Single Server Queue

Asymptotics for Steady-state Tail Probabilities in Structured Markov Queueing Models

In this paper we establish asymptotics for the basic steady-state distributions in a large class of single-server queues. We consider the waiting time, the workload (virtual waiting time) and the steady-state queue lengths at an arbitrary time, just before an arrival and just after a departure. We start by establishing asymptotics for steady-state distributions of Markov chains of M/GI/1 type. ...

A Hyperexponential Approximation to Finite- and Infinite-time Ruin Probabilities of Compound Poisson Processes

This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process. By approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finitetime) ruin probability as a solvable ordinary differential equation (or a partial differential equ...

A Hyperexponential Approximation to Finite-Time and Infinite-Time Ruin Probabilities of Compound Poisson Processes

This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equ...